Being confused of distribution notations in Deep Learning book
At page 130 of the same book, the author states that $\hat{p}_\text{data}$ is an empirical distribution defined by the training data. Similarly, at page 129, he states that $p_\text{data}$ is the true distribution that generates the set $\mathbb{X} = \{ \boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(m)} \}$.

What is the difference between $\hat{p}_\text{data}$ and $p_\text{data}$? You can think of $\hat{p}_\text{data}$ as a histogram that is calculated from the set $\mathbb{X}$ and $p_\text{data}$ as the true distribution from which the elements in $\mathbb{X}$ are drawn. 

The subscript ${\boldsymbol{x}, y \sim \hat{p}_\text{data}}$ in the expectation $\mathbb{E}_{\boldsymbol{x}, y \sim \hat{p}_\text{data}}$ indicates that the expectation is taken with respect to the samples drawn from the empirical distribution $\hat{p}_\text{data}$. In other words, you will optimise the objective function $J$ using the training data. Have a look at this question for more info.

The subscript ${\boldsymbol{x}, y \sim p_\text{data}}$ in the expectation of formula $5.101$ is a typo. In fact, in this online version of the book, at page 151, the subscript of the expectation is  ${\boldsymbol{x}, y \sim \hat{p}_\text{data}}$.